The edge length of the unit cell of a metal ( | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The formula for density is $d = \frac{Z 	imes M_W}{N_A 	imes a^3}$.Given: $d = 1.74 \, g \, cm^{-3}$,$M_W = 24 \, g \, mol^{-1}$,$a = 4.53 \, \m

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(B) The formula for density is $d = \frac{Z 	imes M_W}{N_A 	imes a^3}$.Given: $d = 1.74 \, g \, cm^{-3}$,$M_W = 24 \, g \, mol^{-1}$,$a = 4.53 \, \mathring{A} = 4.53 	imes 10^{-8} \, cm$,and $N_A = 6 	imes 10^{23} \, mol^{-1}$.Rearranging for $Z$: $Z = \frac{d 	imes N_A 	imes a^3}{M_W}$.$Z = \frac{1.74 	imes (6 	imes 10^{23}) 	imes (4.53 	imes 10^{-8})^3}{24}$.$Z = \frac{1.74 	imes 6 	imes 10^{23} 	imes 93.01 	imes 10^{-24}}{24}$.$Z = \frac{1.74 	imes 6 	imes 93.01 	imes 10^{-1}}{24} \approx \frac{971.08}{240} \approx 4.04$.Thus,the effective number of atoms $Z$ is $4$.

The edge length of the unit cell of a metal $(M_W = 24 \, g \, mol^{-1})$ having a cubic structure is $4.53 \, \mathring{A}$. If the density of the metal is $1.74 \, g \, cm^{-3}$,then the effective number of atoms in the unit cell is :- $(N_A = 6 \times 10^{23} \, mol^{-1})$

Similar Questions

Calculate the number of unit cells in $10 \, g$ of $CsCl$ which crystallizes in a $bcc$ structure. $(CsCl = 168.5 \, amu)$

The edge length of a body-centered cubic $(BCC)$ unit cell is $390 \ pm$. If the radius of the cation is $150 \ pm$, what is the radius of the anion? (in $pm$)

Calculate the volume of the unit cell if an element having a molar mass of $180 \ g \ mol^{-1}$ forms an $fcc$ unit cell. $\left[\rho \cdot N_{A} = 120 \times 10^{21} \ g \ cm^{-3} \ mol^{-1}\right]$

An element is found to crystallize with $BCC$ structure having density $8.55 \ g \ cm^{-3}$. What is the edge length of the unit cell? (Atomic mass of element $= 93$)

The number of atoms in $100 \ g$ of an $fcc$ crystal with density $d = 10 \ g/cm^3$ and cell edge equal to $100 \ pm$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module